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(a) shows that every pair of opposite sides in the hexagon a′b′c′d′e′f′ are parallel and equal in length. On the other hand, (b) demonstrates that the triangles a′c′e′ and b′d′f′ have equal areas.

(a) To show that every pair of opposite sides in hexagon a'b'c'd'e'f' are parallel and equal in length, we can use the fact that the centroids of triangles divide the medians into segments of equal length.

Let's consider a'b' and d'e'. The centroid of triangle fab, a', divides the median fb into two segments, a'f and a'b', such that a'f = 2/3 * fb. Similarly, the centroid of triangle def, e', divides the median de into two segments, e'd and e'f', such that e'd = 2/3 * de.

Since fb = de (opposite sides of hexagon abcdef), we have a'f = e'd. Now, we can consider the triangles a'f'd' and e'df'. By the properties of triangles, we know that if two sides of a triangle are equal, and the included angles are equal, then the triangles are congruent.

In this case, a'f' = e'd' (as shown above) and angle a'f'd' = angle e'df' (corresponding angles). Therefore, triangle a'f'd' is congruent to triangle e'df'.

By congruence, the corresponding sides a'd' and e'f' are equal in length.

By similar reasoning, we can show that b'c' and e'f', as well as c'd' and f'a', are parallel and equal in length.

(b) To show that triangles a'c'e' and b'd'f' have equal areas, we can use the fact that the area of a triangle is one-half the product of its base and height.

In triangle a'c'e', the base is c'e' and the height is the perpendicular distance from a' to c'e'. Similarly, in triangle b'd'f', the base is d'f' and the height is the perpendicular distance from b' to d'f'.

Since opposite sides in hexagon a'b'c'd'e'f' are parallel (as shown in part (a)), the perpendicular distance from a' to c'e' is equal to the perpendicular distance from b' to d'f'.

Therefore, the heights of triangles a'c'e' and b'd'f' are equal. Additionally, the bases c'e' and d'f' are equal (as shown in part (a)).

Using the area formula, area = 1/2 * base * height, we can see that the areas of triangles a'c'e' and b'd'f' are equal.

Hence, we have shown that triangles a'c'e' and b'd'f' have equal areas.

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Answer:

The margin of error is multiplied by 1.41, which is 1 divided by the square root of 5.

Step-by-step explanation:

The margin of error is:

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which z is related to the confidence level, \(\sigma\) is the standard deviation of the population and n is the size of the sample.

The margin of error is inverse proportional to the square root of the sample size.

Then

Sample size n:

\(M = z*\frac{\sigma}{\sqrt{n}}\)

Modified(half the sample size):

\(M_{M} = z*\frac{\sigma}{\sqrt{0.5n}}\)

Ratio

\(\frac{M_{M}}{M} = \frac{z*\frac{\sigma}{\sqrt{0.5n}}}{z*\frac{\sigma}{\sqrt{n}}} = \frac{\sqrt{n}}{\sqrt{0.5n}} = \frac{\sqrt{n}}{\sqrt{0.5}*\sqrt{n}} = \frac{1}{\sqrt{0.5}} = 1.41\)

The margin of error is multiplied by 1.41, which is 1 divided by the square root of 5.

Answer:

The vertex is located on the x-axis between the second and third quadrants

Step-by-step explanation:

Whereby the function is f(x) = (x + 3)², we have;

f(x) = (x + 3)² = x² + 6·x + 9

The vertex, (h, k), of the quadratic function given in general form, a·x² + b·x + c is found as follows;

h = -b/(2·a) and k = f(h)

Therefore by comparison of the given quadratic function and the general form of a quadratic function, we have;

a = 1, b = 6, c = 9

h = -6/(2 × 1) = -3

k = f(-3) = (-3)² + 6 × (-3) + 9 = 0

The vertex (h, k) = (-3, 0)

Therefore, the location of the vertex is on the x-axis axis between the second and the third quadrant.

Answer:

0 , 3

Step-by-step explanation:

please see above first square is 0 and 2nd 3

Planets around other stars can be detected by carefully measuring the "brightness" or "light intensity" of stars.

When a planet orbits a star, it causes a slight change in the brightness or light intensity of the star. This is known as the transit method of planet detection. As the planet passes in front of the star from our line of sight, it blocks a small portion of the star's light, causing a temporary decrease in its brightness. By carefully measuring these changes in brightness over time, scientists can infer the presence and characteristics of planets orbiting the star. This method has been instrumental in the discovery of numerous exoplanets in recent years.

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Answer:

120 mg

Step-by-step explanation:

20% of  100 is 20 so that would be 20mg  plus the 100mg they just took

100+20=120mg

i hope this helps you!

The coefficient of determination for a linear regression model fitting with bivariate dataset ( scatterpot present in above figure) is equals to the 90.097.

When we study about linear regressions, usually analyze two coefficients that help us to know about the quality of the regression model and strength of linear relationship between the variables. One is called the coefficient of determination, denoted by R². Consequently, by observing a scatter plot, we can estimate the value of these coefficients. We have a scatterpot for a linear model fitting of the bivariate dataset is present in above figure. Coefficient of determination is always positive. When data are very closely arranged along a approximate line, then coefficient of determination is more near to 1 (In percentage it is 100). Here points are almost closely arranged . So percentage should be near to 100. So possible answer is 90.097. Hence, the answer is 90.097.

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Complete question :

The above figure complete the question.

What is the coefficient of determination for a linear model fitting the following bivariate dataset?

Allura, this is the solution:

As you can see we have two right triangles in the figure:

Therefore,

Step 1: Let's calculate the hypotenuse of the left triangle, as follows:

c² = a² + b²

c² = 12² + 18²

c²= 144 + 324

c² = 468

c = 21.63

Step 2: Let's calculate the sides of the right triangle on the right, this way:

Leg 1 = 21.63

Leg 2 = x

Hypotenuse = 12 + y

Height of the right triangle = 18

In consequence, to find the value of the hypotenuse and y, we have:

c = 21.63²/√21.63² - 18²

c = 468/√468 - 324

c = 468/12

c = 39

Step 3: Now, we can solve for y, this way:

39 = 12 + y

y = 39 - 12

y = 27

The correct answer is D. 27

Answer:

-3

Step-by-step explanation:

Let the number be x.

x^2 - 21 = 4x

x^2 - 4x - 21 = 0

(x - 7)(x + 3) = 0

x - 7 = 0 or x + 3 = 0

x = 7 or x = -3

Answer: -3

Answer:

-3

Step-by-step explanation:

I got it right

Answer:

The car travelled an average speed of 80 km/h.

Step-by-step explanation:

Distance travelled by the car = 160 km

Time taken by the car = 2 hours.

Average speed =?

Average speed = Distance/Time

Average speed = 160/2

Average speed = 80 km/h

The car travelled an average speed of 80 km/h.

A Colorado blue spruce's first ten years have an average diameter of 0.62 inches.

Measure the diameter of the tree in its first ten years and divide it by 10 to determine the average diameter of a Colorado blue spruce in its first ten years. The outcome is the tree's average diameter during its first ten years. Measure the diameter of the tree in its first ten years and divide it by 10 to determine the average diameter of a Colorado blue spruce in its first ten years. The outcome is the tree's average diameter during its first ten years. For instance, if a Colorado blue spruce is five years old, you would calculate its diameter and multiply it by 10. You will then know the tree's typical diameter for the first ten years. Any age of Colorado blue spruce tree can use the same calculation. Depending on the age of the tree, a Colorado blue spruce's first ten years' average diameter will vary. The average diameter will be greater if the tree is older than ten years. The average diameter will be less, however, if the tree is less than 10 years old. In general, a Colorado blue spruce's first ten years have an average diameter of 0.62 inches.

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Answer: -8x-6y-10

Step-by-step explanation:

The expression (-4x-3y-5)2 is equivalent to the expression - 8x - 6y - 10 none of the options are correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

= (-4x-3y-5)2

After using the distributive property:

= - 8x - 6y - 10

Thus, the expression (-4x-3y-5)2 is equivalent to the expression - 8x - 6y - 10 none of the options are correct.

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Answer:

B) 0.7

Step-by-step explanation:

You put 70% into fraction form, 70/100. Then you divide 70 by 100 giving you 0.7

Answer:

It will take Ryan 59.6 years to break even on his purchase of 3 discount points (1% each) for a $520,000 loan with an APR of 4.15%. This break-even point was calculated by finding the difference in monthly payments between the loan with and without the discount points, and dividing the cost of the points by that difference.

Answer:

The maximum amount of people that can go to the amusement park is 15.

Step-by-step explanation:

First you create an equation to represent the question

8.75+25.75x≤420

You put the less than or equal to sign because 420 is the maximum amount of money.

Now you just solve the equation.

25.75x≤420-8.75

25.75x≤411.25

x≤411.25/25.75

x≤15.9708738

Then you have to round down because you cant have .9 of a person.

So x≤15

Then, Check your solution

8.75+(25.75 x 15)≤420

8.75+386.25≤420

395≤420

That is true. But to make sure that is the maximum add another 25.75

395+25.75≤420

420.75≤420

This is equation is false so, our answer is correct.

The maximum amount of people that can go to the amusement park is 15.

Answer:

5190

Step-by-step explanation:

2.7% of 6000 is 162.

There is a 5 year span between 2009 and 2014.

So just subtract 162 from 6000 5 times, or multiply 162 by 5, then subtract that from 6000.

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The amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

What is amount and example?

amount to (something) : to produce (a total) when added together. The bill amounted to 10 dollars. They have debts amounting to thousands of dollars.

To calculate the amount of wood, in meters, needed to rebuild the frame, we can use the following formula:

wood (m) = (wood (ft) x 0.3048) / 6

Since each piece of wood provided measures 6 ft (approximately 1.8 to 8.7), we can calculate the amount of wood, in meters, needed to rebuild the frame as follows:

wood (m) = (6 ft x 0.3048) / 6

wood (m) = 1.8288 m      

Therefore, the amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

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The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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Let be x the amount the owner withdrew. Then, we can write and solve the following equation:

Answer

The owner withdraws $2,000.

Answer:

x + y = 1042

1.50x + 0.75y = 1140

Step-by-step explanation:

If there was a total of 1,042 fares paid then x + y would be equal to that because x is the number of regular fares paid and y is the number of reduced fares paid.

If there was a total of $1,140 made from the fares then we can use 1.50x + 0.75y. We put the 1.5 in front of the x because each fare paid costs $1.50, same with Y each reduced fare paid is $0.75. So both of those need to be added up to get $1,140.

Answer:

hmm i'm not sure

Step-by-step explanation:

sorry

Answer:

Step-by-step explanation:

Given the expression  5 p + 6 = 7, to know the value of variable p. we need to make p the subject of the formula as shown;

Given  5 p + 6 = 7

Step 1: Subtract 6 from both sides

5p+6-6 = 7-6

5p = 7-6

Step 2: We will then divide both sides by the coefficient of p i.e 5 to have;

5p/5 = (7 - 6)/5

p =  (7 - 6)/5

Hence, the correct expression of variable p is p = (7 - 6)/5

Answer:

Following are solutions to the given question:

Step-by-step explanation:

First-test probability: \(\frac{3}{4}\)

A person's chances of passing a second test are reduced if he fails the first test: \(\frac{1}{3}\)

However, the chance of failing the first test is 1 in 4. As just a result, the probability of these events is low.

\(\to \frac{1}{4}\times \frac{1}{3}=\frac{1}{12}\\\\\to \frac{3}{4} + \frac{1}{12} = \frac{9+1}{12} = \frac{10}{12} = \frac{5}{6}\)

One of the other.

Approximately 58.33% of the workers in the group are making over $25 an hour. The percentage was obtained by finding the area under the uniform distribution curve above the value of $25.

Since the hourly wages of the workers are uniformly distributed on the interval [20, 32], the probability density function is constant on this interval. The area under the probability density function between any two points a and b gives the probability that a randomly chosen worker's wage will be between a and b. Therefore, the probability that a worker's wage is above $25 is given by the area under the probability density function from 25 to 32, which is (32-25)/(32-20) = 7/12 or approximately 58.33%. Thus, approximately 58.33% of the workers are making over $25 an hour.

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Answer:

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

Step-by-step explanation:

\(\huge\textsf{Hey there!}\)

\(\mathsf{8u^8 + (-21u^8)}\\\mathsf{= 8u^2 - 21u^8}\\\large\textsf{COMBINE the LIKE TERMS}\\\mathsf{=(8u^8 - 21u^8)}\\\mathsf{= 8 - 21\rightarrow\boxed{\bf -13}}\\\mathsf{= 8u^2 - 21u^8 \rightarrow \bf -13u^8}\\\\\\\\\boxed{\boxed{\large\textsf{Answer: \bf -13u}\bf ^2}}\huge\checkmark\\\\\\\\\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\\frak{Amphitrite1040:)}\)

Answer:

The area is 45 inches

Step-by-step explanation:

L×W=A

If number of nickels is 2 more than number of dimes, then she have  42 dimes and 44 nickels.

Let us assume that Taylor has "x" dimes,

So, the number of nickels will be = "x + 2" nickels.

The value of each dime is $0.10, so, total value of dimes is : 0.10x dollars.

The value of each nickel is $0.05, so total-value of nickels is : 0.05(x + 2) dollars.

we also know that, the total value of the coins is $6.40.

So, the equation can be written as :

0.10x + 0.05(x + 2) = 6.40

Simplifying the equation,

We get,

0.10x + 0.05x + 0.10 = 6.40

0.15x + 0.10 = 6.40

0.15x = 6.40 - 0.10

0.15x = 6.30

x = 6.30/0.15

x = 42

So, Taylor has 42 dimes. Now we can find the number of nickels:

Number of nickels = x + 2 = 42 + 2 = 44

Therefore, Taylor has 42 dimes and 44 nickels.

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The given question is incomplete, the complete question is

Taylor has $6.40 in dimes and nickels in her car. The number of nickels is two more than the number of dimes.

How many of each type of coin does she have?